For parabola, y 2 = –12x, what is the length of the latus rectum?

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Given y? = - 12x

The above equation is involving y?

Its axis is x - axis

Also coefficient of x is negative (-12)

Hence we use equation

y? = - 4ax

Comparing

y2=-12x....(1) [Given]

y2= - 4ax

From (1) and (2)

- 12x = - 4ax

4ax = 12x

a = 3

Coordinates of focus is (-a,0)
i.e focus (-3,0)

Equation of directix is

X = a

x = 3

Latus rectum = 4a

= 4 x 3
= 12 Answer
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